Circuit Double Cover of Graphs

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Cambridge University Press, Apr 26, 2012 - Language Arts & Disciplines - 357 pages
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The famous Circuit Double Cover conjecture (and its numerous variants) is considered one of the major open problems in graph theory owing to its close relationship with topological graph theory, integer flow theory, graph coloring and the structure of snarks. It is easy to state: every 2-connected graph has a family of circuits covering every edge precisely twice. C.-Q. Zhang provides an up-to-date overview of the subject containing all of the techniques, methods and results developed to help solve the conjecture since the first publication of the subject in the 1940s. It is a useful survey for researchers already working on the problem and a fitting introduction for those just entering the field. The end-of-chapter exercises have been designed to challenge readers at every level and hints are provided in an appendix.
 

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Contents

Faithful circuit cover
10
Circuit chain and Petersen minor
21
Small oddness
35
Spanning minor Kotzig frames
45
Strong circuit double cover
66
Spanning trees supereulerian graphs
83
Flows and circuit covers
96
Girth embedding small cover
112
Shortest cycle covers
163
Beyond integer 12weight
189
Petersen chain and Hamilton weights
199
Appendix A Preliminary
243
Appendix B Snarks Petersen graph
252
Integer flow theory
273
Hints for exercises
285
Glossary of terms and symbols
322

Compatible circuit decompositions
117
Other circuit decompositions
134
Orientable cover
153
References
337
Author index
351
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About the author (2012)

Cun-Quan Zhang is Eberly Distinguished Professor of Mathematics at West Virginia University.

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